Question

prove that 9 root 5 is an irrational number​

Answer 1

it is from real Number chapter of the 0th class

Answer 2

Answer:

Step-by-step explanation:

Given: 9√5

We need to prove that 9√5 is irrational

Proof:

Let us assume that 9√5 is a rational number.

Sp it t can be expressed in the form p/q where p,q are co-prime integers and q≠0

⇒9√5=p/q

On squaring both the sides we get,

⇒=p²/q²

⇒405q²=p² —————–(i)

p²/405= q²

So 4055 divides p

p is a multiple of 4055

⇒p=405m

⇒p²=164025m² ————-(ii)

From equations (i) and (ii), we get,

405q²=164025²

⇒q²=405m²

⇒q² is a multiple of 405

⇒q is a multiple of 9√5

Hence, p,q have a common factor 9√5. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number

9√5 is an irrational number

Hence proved

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